1.
$\begin{align*}
{{47x}\over{18}}+{{4}\over{9}} &= {{7x}\over{3}}+{{17}\over{18}} && |\cdot 18\\
47x+8 &= 42x+17 && |-\left(42x+8\right)\\
5x &= 9 && |:5\\
x &= {{9}\over{5}}
\end{align*}$
2.
$\begin{align*}
2x+{{5}\over{4}} &= {{5x}\over{3}}+{{3}\over{2}} && |\cdot 12\\
24x+15 &= 20x+18 && |-\left(20x+15\right)\\
4x &= 3 && |:4\\
x &= {{3}\over{4}}
\end{align*}$
3.
$\begin{align*}
{{62x}\over{21}}+{{5}\over{3}} &= {{8x}\over{3}}+{{43}\over{21}} && |\cdot 21\\
62x+35 &= 56x+43 && |-\left(56x+35\right)\\
6x &= 8 && |:6\\
x &= {{4}\over{3}}
\end{align*}$